Already a known quantity in underground music circles thanks to his work with the free-form collective known as No Neck Blues Band and his country-folk project D. Charles Speer and the Helix, the Greenpoint multi-instrumentalist is attracting some mainstream interest via his new project Rhyton.

The instrumental trio, which is playing Union Hall in Williamsburg on Dec. 10, combines Shuford’s primary musical interests — psychedelic rock and traditional sounds from Greece and the Middle East — into a heady and hypnotic blend.

That might sound like enough to pique the interest of most music critics, but it wasn’t until the band released its third album “Kykeon” this year that it really captured the attention of the cool music cognoscenti, garnering write-ups from hip publications including Noisey and Paste Magazine. That may be because for the first time, the group is using structured songs rather than the improvisational focus that marked its previous releases.

“It was just a process of trying to explore options and possibilit­ies,” Shuford said of the band’s new songwriting approach. “It was a way to keep it interesting for ourselves and have some contrasting moods for our live shows.”

Shuford also keeps things stimulating by utilizing the bouzouki and the saz, stringed instruments that date back to the mid-18th century and are ancestors of the guitar. Shuford said his interest in these tools has helped connect him to both his Greek ancestry and his musical curiosity.

“Once you learned the scales and harmonic structures that worked for those instruments, it opens up some new avenues of technique that I never would have thought to engage with,” he said.

But while all the newfound interest in his art is an exciting turn of events, Shuford said it also comes at a more complicated time for him and bandmates bassist Jimy SeiTang and drummer Rob Smith. Namely, they are not as young as they used to be.

“It’s harder to organize people when they get older,” said Shuford. “When both they and myself have families, it’s not as easy to be able to drop everything and say, ‘Let’s go do this weird thing for six hours on Saturday.’ ”

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